PROBLEM 4S.8
KNOWN
:
Twodimensional, square shapes, 1 m to a side, maintained at uniform temperatures as
prescribed, perfectly insulated elsewhere.
FIND
:
Using the flux plot method, estimate the heat rate per unit length normal to the page if the thermal
onductivity is 50 W/m
⋅
K
c
ASSUMPTIONS
:
(1) Steadystate, twodimensional conduction, (2) Constant properties.
ANALYSIS
:
Use the methodology of Section 4S.1 to construct the flux plots to obtain the shape factors
from which the heat rates can be calculated.
With Figure (a), begin at the lowerleft side making the
isotherms almost equally spaced, since the heat flow will only slightly spread toward the right.
Start
sketching the adiabats in the vicinity of the T
2
surface.
The dashed line represents the adiabat which
separates the shape into two segments.
Having recognized this feature, it was convenient to identify
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 Spring '10
 LEE,J.S.
 Thermodynamics, Heat, Heat Transfer, shape factors, flux plot

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